New Wald Test Compared with Chen and Fienberg's for Testing Independence in Incomplete Contingency Tables

In $I{\times}J$ incomplete contingency tables, the test of independence proposed by Chen and Fienberg(1974) uses $I{\times}J-1$ instead of (I-1)(J-1) degrees of freedom without providing much of an increase in the value of the test statistic. For these reasons, Chen and Fienberg tests are expected to have less power. New Wald test statistic related to the part of Chen and Fienberg test statistic is proposed using delta method. These two tests are compared through Monte Carlo studies.